Estimating subnational excess mortality in times of pandemic. An application to French départements in 2020

The COVID-19 pandemic’s uneven impact on subnational regions highlights the importance of understanding its local-level mortality impact. Vital statistics are available for an increasing number of countries for 2020, 2021, and 2022, facilitating the computation of subnational excess mortality and a more comprehensive assessment of its burden. However, this calculation faces two important methodological challenges: it requires appropriate mortality projection models; and small populations imply considerable, though commonly neglected, uncertainty in the estimates. We address both issues using a method to forecast mortality at the subnational level, which incorporates uncertainty in the computation of mortality measures. We illustrate our approach by examining French départements (NUTS 3 regions, or 95 geographical units), and produce sex-specific estimates for 2020. This approach is highly flexible, allowing one to estimate excess mortality during COVID-19 in most demographic scenarios and for past pandemics.

Instead of considering pre-pandemic mortality levels as the baseline in absence of COVID-19, we opted to forecast mortality in 2020 extrapolating mortality temporal changes.Among the numerous forecasting mortality methods, we rely on CP -splines (Camarda, 2019) given the numerous advantages in terms of statistical robustness and flexibility.However, the recent development of this methodology has prompted the reviewers to ask for a comparison to an alternative approach.
A comprehensive comparison of various mortality forecasting methods goes beyond the purpose of this paper and appendix, as it has already been covered elsewhere1 .Here, our focus is on the Lee-Carter model (Lee and Carter, 1992), which serves as a benchmark approach for forecasting mortality.In a nutshell, the Lee-Carter model utilizes principal components to describe the evolution of mortality over age and time.This simplifies the problem from a two-dimensional perspective to standard mortality age-pattern, a fixed-age effect and a univariate time index.The time index captures historical changes in mortality, and it is extrapolated using time-series analysis to forecast future mortality.For a more thorough understanding of this model and its relevance in mortality forecasting, please refer to the work of Basellini et al. (2023).
In order to maintain a consistent and appropriate stochastic framework for mortality data, we made the decision to estimate the Lee-Carter model using a Poisson setting, as described in Brouhns et al. (2002).As a result, any discrepancies between the two approaches will solely arise from a different functional form used to describe mortality developments.
Figure 1 illustrates the comparison of the two approaches in terms of losses in male life expectancy at age 60 in 2020 for each French département.The outcomes show a considerable similarity, particularly for larger geographical subunits.With only a few exceptions, the losses estimated by the Lee-Carter model fall within the 95% confidence intervals of those estimated by CP -splines.As a result, we have confidence that employing a different approach would not significantly alter our final conclusions.

Lee-Carter
Figure 1: Losses in male life expectancy at age 60 in 2020 for each French département.Colored dots depict point-estimates for CP -splines (orange) and Lee-Carter model (red).Horizontal bars represent represent 95% level confidence interval for CP -splines.In bold the four départements with the largest differences between the two forecasting approaches.
To conduct a more detailed comparison, we focus on four départements where the discrepancies in losses between the Lee-Carter and CP -splines approaches are the largest: Tarn, Lozère, Alpes de Haute Provence and Belfort.These regions are depicted in bold in Figure 1. Figure 2 displays the observed and estimated life expectancy at age 60 for both methods in these specific geographical areas.As outlined in the paper, we optimize the starting period for each subunit, perform estimation up to 2019, and forecast for 2020.The 95% confidence intervals are depicted for both approaches.
While the CP -splines automatically provide uncertainty measures for both observed and forecast years, the default Lee-Carter model only offers uncertainty measures for future years.Upon analyzing the figure, it becomes evident that the Lee-Carter model is overfitting the e 60 data, and its forecast can be regarded as somewhat inaccurate.Consequently, the relatively large differences in losses compared to the CP -spline estimates can be attributed to the subpar performance of the Lee-Carter model in these départements.

Lozère Tarn
Alpes de Haute Provence Belfort 1970197519801985199019952000200520102015202019701975198019851990199520002005   The proposed model exhibits an additional advantage that becomes apparent when examining the mortality age-pattern for a specific year.In Figure 3, both the observed and forecast log-rates in 2020 are depicted for the mentioned four départements, using both the Lee-Carter and CP -splines approaches.The Lee-Carter estimates display a wiggling behavior, in stark contrast to the smoother patterns fitted by CP -splines.
Despite the Lee-Carter model's unreasonableness, summary measures like life expectancy might conceal these erratic forecast age-patterns.However, when losses are measured by indicators for specific ages, this erratic behavior can have a detrimental effect.In contrast, CP -splines demonstrate robustness and are exempt from such unrealistic behaviors.
in male life expectancy at 60 in 2020 (years)

Figure 2 :
Figure 2: Observed, estimated and forecast life expectancy at age 60, produced by both the CP -splines and Lee-Carter methods for four specific French départements where the differences in estimated 2020 losses in e 60 between the two approaches are the largest.Starting year optimized for each département, estimated up to 2019 and forecast in 2020.

Figure 3 :
Figure3: Forecast age-specific log-rate for the year 2020, produced by both the CP -splines and Lee-Carter methods for four specific French départements where the differences in estimated 2020 losses in e 60 between the two approaches are the largest.